Symmetrization in analysis
Author(s)
Bibliographic Information
Symmetrization in analysis
(New mathematical monographs, 36)
Cambridge University Press, 2019
- : hardback
Available at 9 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. [454]-468) and index
Description and Table of Contents
Description
Symmetrization is a rich area of mathematical analysis whose history reaches back to antiquity. This book presents many aspects of the theory, including symmetric decreasing rearrangement and circular and Steiner symmetrization in Euclidean spaces, spheres and hyperbolic spaces. Many energies, frequencies, capacities, eigenvalues, perimeters and function norms are shown to either decrease or increase under symmetrization. The book begins by focusing on Euclidean space, building up from two-point polarization with respect to hyperplanes. Background material in geometric measure theory and analysis is carefully developed, yielding self-contained proofs of all the major theorems. This leads to the analysis of functions defined on spheres and hyperbolic spaces, and then to convolutions, multiple integrals and hypercontractivity of the Poisson semigroup. The author's 'star function' method, which preserves subharmonicity, is developed with applications to semilinear PDEs. The book concludes with a thorough self-contained account of the star function's role in complex analysis, covering value distribution theory, conformal mapping and the hyperbolic metric.
Table of Contents
- Foreword Walter Hayman
- Preface David Drasin and Richard S. Laugesen
- Introduction
- 1. Rearrangements
- 2. Main inequalities on Rn
- 3. Dirichlet integral inequalities
- 4. Geometric isoperimetric and sharp Sobolev inequalities
- 5. Isoperimetric inequalities for physical quantities
- 6. Steiner symmetrization
- 7. Symmetrization on spheres, and hyperbolic and Gauss spaces
- 8. Convolution and beyond
- 9. The *-function
- 10. Comparison principles for semilinear Poisson PDEs
- 11. The *-function in complex analysis
- References
- Index.
by "Nielsen BookData"